Metro Transit Presentation

Our Approach to the Data

• Logarithmic transformation of the data to account for right skew

Variable Relationships

• X lables have been added to correlations with p values \(\geq\) 0.01
• What are the relationships between the variables we have been given?

Exploratory Analysis

• A look at our initial linear regression model
• Dwell is affected differently depending on the form of payment

Interactions

• What happens to cash when lift is cycled vs when it isn’t?  
• We included interaction terms to help account for these differences

Group Differences: line_id & site_id

• Site_id and line_id have particularly drastic differences in terms of mean dwell time
• Site_id has a strong relationship with time and the pay-leave pay class

Spatial Relationships

• The stops with the highest mean dwell time appear randomly distributed  
• More customers pay using Go-To cards on the outside the city centers

Random Effects

##  Groups           Name               Std.Dev. Corr         
##  site_id:hourTime (Intercept)        0.123091              
##                   pay_classOffboard  0.120095 -1.000       
##                   pay_classPay-leave 0.076287  0.322 -0.325
##  site_id          (Intercept)        0.142895              
##                   pay_classOffboard  0.074281 -1.000       
##                   pay_classPay-leave 0.237770  0.148 -0.129
##  line_id          (Intercept)        0.078416              
##  hourTime         (Intercept)        0.056950              
##                   pay_classOffboard  0.035387 -0.881       
##                   pay_classPay-leave 0.012109 -0.986  0.789
##  Residual                            0.479430

• Based on the previous two slides, there are clear observable differences
  between the two groups (site_id and line_id)
  • Based on these observations we believe that there is an underlying hierarchical
    structure to the data
• 4 random effects: site_id, line_id, time (hour of the day), and time*site_id

Regression Results: Coefficients and Standard Errors

Model Limitations

• There are clear disagreements between the models
• In particular, pay class and interactions with the variable
  • We are hesitent to fit our model on the combined data

Data Constraints

• Limited time frame (only 2 weeks of data)
  
• What other trends might we see with more data?

Weather Constraints

• The only data we added was weather, which was fairly similar across the two weeks
  • We may want to consider other variables in the future

Conclusion

• Our model is an inferential model, not a predictive model
• We hope to illustrate that certain variables and the interaction
  between them lead to quite different effects on mean dwell time
• With the input of more data, Metro Transit’s team would be able to
  develop a model capable of prediction

Thank You! Questions?

• Thank you to Prof. Andy Poppick and Eric Lind